A220298 Number of ways to cut a 5 X n rectangle into rectangles with integer sides.

1, 16, 650, 31484, 1613060, 84231996, 4427635270, 233276449488, 12300505521832, 648782777031100, 34223109012944482, 1805323555104984956, 95234889270955121716, 5023877415526067785580, 265022449692240368203598, 13980623266954069411358904

Offset: 0

Author

Alois P. Heinz, Dec 10 2012

Keywords

• nonn

Examples

			a(1) = 16:
  ._. ._. ._. ._. ._. ._. ._. ._. ._. ._. ._. ._. ._. ._. ._. ._.
  | | |_| | | | | | | |_| |_| |_| | | | | | | |_| |_| |_| | | |_|
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  |_| |_| |_| |_| |_| |_| |_| |_| |_| |_| |_| |_| |_| |_| |_| |_|
.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200
• David A. Klarner and Spyros S. Magliveras, The number of tilings of a block with blocks, European Journal of Combinatorics 9 (1988), 317-330.
• Joshua Smith and Helena Verrill, On dividing rectangles into rectangles

Crossrefs

Column m=5 of A116694.

Programs

Maple

gf:= (39672144*x^10 -110891556*x^9 [phone]*x^8 -74544838*x^7 [phone]*x^6 -5961522*x^5 +841659*x^4 -73608*x^3 +3769*x^2 -100*x+1)/
(135762480*x^10 -326041524*x^9 [phone]*x^8 -170972730*x^7 [phone]*x^6 -11002298*x^5 +1395665*x^4 -109292*x^3 +4975*x^2 -116*x +1):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..20);

Formula

G.f.: see Maple program.